Can someone explain how to do this

  C)  12

Step-by-step explanation:

You can do this several ways:

1. (My favorite) Graph it using a graphing calculator. (See attached.) The graph shows the maximum value is 12.

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2. Evaluate the function at the vertex. Of course, you have handy reference to the formula for the location of the vertex of y=ax^2+bx+c. It is ...

  x = -b/(2a)

For a=-2, b=-8, this becomes x=-(-8)/(2(-2)) = 8/-4 = -2

Evaluating the function at x = -2, we find ...

  y = -2(-2)^2 -8(-2) +4 = -8 +16 +4 = 12

The maximum value of the function is 12.

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3. Rewrite the function to vertex form and read the maximum from the equation.

  y = -2(x^2 +4x) +4 . . . . . . . . . factor the leading coefficient from the first two terms

  y = -2(x^2 +4x +4) +4 -(-2(4)) . . . . add the square of half the x-coefficient inside parentheses; subtract the same amount outside

  y = -2(x +2)^2 +12 . . . . . . simplify to vertex form: y = a(x -h)^2 +k for vertex (h, k)

The vertex is (-2, 12), so the maximum value is 12.

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step-by-step explanation:

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